Provided is a robotic system that includes a surgical instrument with a wrist that allows N degrees of freedom of movement. The N degrees of freedom can be controlled by N+1 cable segments. The wrist can include a first set pulleys configured to rotate about a first axis and a second set of pulleys configured to rotate about a second axis. The wrist can further comprise one or more pulleys configured to engage two of the cable segments, wherein at least one of the pulleys is shared by a first cable segment and a second cable segment. The first cable segment and the second cable segment that share the pulley can be independent from one another. In some circumstances, the surgical instrument can be actuated in N+1 degrees of movement by advancing or retracting at least two of N+1 cable segments.
